Many known non-linear dynamic maps follow similar behavioral patterns such as periods of double cascading and islands of stability before reaching the fully developed chaotic regimes. The paper introduces a novel family of parametric generalized tent maps that do not follow the above route to chaos. Instead of forming well defined and observable cascading patterns, all cyclic structures become dynamically unstable with bifurcation branches scattered inside narrow subdomains that can overlap. The method of Lyapunov Exponent is applied to characterize transitions to chaotic regimes. The paper demonstrates the ergodic property of the dynamic process by computing invariant distributions of the map. A closed-form distribution for the developed chaos is derived. A zone of instability exists where ergodic property fails.